Network representation of cardiac interbeat intervals for monitoring restitution of autonomic control for heart transplant patients

2.5 MB·English

by  Danuta Makowiec

PROCEEDINGSOFTHE7THESGCO2012,APRIL22-25,2012,KAZIMIERZDOLNY,POLAND 1
Network representation of cardiac interbeat intervals
for monitoring restitution of autonomic control for
heart transplant patients.
Danuta Makowiec, Stanisław Kryszewski, Beata Graff, Joanna Wdowczyk-Szulc, Marta Z˙arczyn´ska-
Buchnowiecka, Marcin Gruchała and Andrzej Rynkiewicz
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1 Abstract—The aim is to present the ability of a network of intervals between subsequent cardiac contractions in patients
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transitions as a nonlinear tool providing a graphical represen- after HTX.
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tation of a time series. This representation is used for cardiac
We will also raise the question whether these transitions

n RR-intervalsinfollow-upobservationofchangesinheartrhythm
build a monotonic sequence of accelerations or decelerations.
a of patients recovering after heart transplant.
We are of opinion that sequences of monotonic accelerations
J
Index Terms—heart transplant, heart rate variability, graphi- ordecelerationsmayindicateresponseofthecardiacsystemto
6 cal representation
somespecialneedsoftheorganism.Hence,thesestudiesmay

] have a chance to offer additional insights into the emergence
n
of the heart regulatory control.
a I. INTRODUCTION
- It must be emphasized that all graphical representations of
a The patient’s life is usually endangered before the decision the discussed networks are produced with the Pajek software
t
a to transplant the heart is taken. On the other hand, in many package [7].
d cases it is amazing how the patient’s organism recovers after
.
s heart transplant (HTX) [1].
c II. METHODS
It is generally believed that the time intervals between sub-
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s sequent heart contractions (so-called RR-intervals) carry the A. The patient group
y
informationaboutthecardiaccontrolsystemmainlydrivenby We analyze 24-hour sequences of 23 ECG signals com-
h
p autonomic nervous system [2]. However, heart transplantation prising of the intervals between two successive R waves of
[ interrupts the possibility of autonomic control over the heart sinus rhythm. These signals were taken from 11 patients

beating. Therefore, heart rate variability (HRV) in patients recovering after heart transplantation in the First Cardiology
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v afterHTXislow,regardlessofthetimeelapsedsincesurgery. Clinic of Gdan´sk Medical University. The recordings were
3 It is controversial whether the cardiac reinnervation occurs taken from the same patients within different periods after
2 afterHTX[1].Butitisexpectedthatprogressivereinnervation surgery. Therefore, we have 3 recording from two patients, 2
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sets in and it is a good prognosis for survival. recordings from 8 patients and 1 recording from one patient.
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We believe that the changes that occur in heart rhythm We considered signals taken from two weeks to 38 months
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1 may provide the first signals of the recovery of cardiac after HTX.
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control. Furthermore, these signals should be connected with FromeachRR-signalwehavecarefullyselectedasequence
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the increasing influence of the sympathetic nervous system. of 15,500 points corresponding to nocturnal rest of a patient.
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: Thereforewehopethatobservingthesechanges,withthehelp There are two reasons why we investigate the nocturnal heart
v
of carefully selected tools, we can describe the process of rhythm. The first one is that during the sleep the central
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X cardiac reinnervation. nervous system is less dependent on the patient’s intentions,
r The considerable success of the network theory in various and therefore we may have a more direct insight into reflexes
a
fields of research (see, e.g., [3], [4]) motivated us to explore regulatingthecardiacrhythm.Moreover,thenocturnalrecord-
these ideas in the analysis of HRV time series. Tools of ings appear to be less perturbed by artifacts what enables us
the complex networks allow one to resolve important and to study sufficiently long and consistent signals.
complementary properties of a dynamical system. For ex- To avoid influence of artifacts (errors in detecting the R-
ample, it is possible to study spatial dependencies between wave)theconsecutiveRR-intervalswerethoroughlyreviewed.
individual observations instead of temporal correlations. In The parts, which consist of at least 500 normal-to-normal
the following we continue our earlier studies (see [5]) on intervals, were identified. If two such parts were separated by
networks of transitions applied to study recordings of time artifacts or ectopic beats of the length smaller than 10, then
the gap was edited manually. To preserve time chronology,
DanutaMakowiecandStanisławKryszewskiarewithGdan´skUniversity, thecorrespondingRR-intervalswereinterpolatedbythevalue
Poland,e-mail:fi[email protected]. of median from the last normal-to-normal seven events. Ad-
Beata Graff, Joanna Wdowczyk-Szulc, Marta Z˙arczyn´ska-Buchnowiecka,
ditionally, the value of median was confronted with the total
MarcinGruchałaandAndrzejRynkiewiczarewithGdan´skMedicalUniver-
sity,Poland. length of the edited gap.
PROCEEDINGSOFTHE7THESGCO2012,APRIL22-25,2012,KAZIMIERZDOLNY,POLAND 2
B. Network representation of RR-signal
In general, the construction of the transition network [3]
is based on the concept of phase space. The phase space
represents all possible values of studied dynamical system
partitioned into mutually disjoint sets. Since the recorded
values of RR-intervals have well-separated magnitudes then
partitioning of the value space of RR-intervals is natural.
Assuming these values as vertices of a network, we represent
each pair of consecutive in time RR-intervals as a transition
between these vertices.
Fig.2. Typicalnetworksobtainedforapatient(here,calledloj)whenthe
patientwas4(left)and38(right)monthsafterHTX.Forbetterreadabilitythe
transitionswithprobabilitylessthan0.1%areomittedbutallverticeswhich
correspond to all recorded RR-intervals are plotted. The widths of arrows
representlogarithmsofcountsoftheparticulartransitions.
use the following coloring scheme:
– no change in the value, i.e., RR =RR : violet;
i i+1
– to a nearest neighbor, i.e., |RR −RR |=∆ : green;
i i+1
– to a next neighbor, i.e., |RR −RR |=2∆ : blue;
i i+1
– to a second neighbor, i.e., |RR −RR |=3∆ : red;
i i+1
– to other neighbors, i.e., |RR −RR |>3∆ : black.
i i+1
Fig. 2 shows two transition networks obtained for a patient
called loj. The left network represents heart rhythm after 4
months elapsed after HTX, the rigth one 34 months later. The
Fig.1. Constructionofanetworkfromatimeseries.Left:spacevaluesfrom important message of this example is that when the time after
atimeseriesdiscretizedat∆=10msec.Right:atimeseriesasapathona
HTX increases the number of transitions other than to nearest
networkofvaluesofphasespace.
neighbors also increases (in the right panel there are more red
and black arrows). We believe that it is a good symptom.
More precisely, the N values of a recording with RR-
It should be explained that widths of the transition arrows
intervals {RR ,RR ,...,RR } are uniformly discretized
1 2 N
in Fig. 2 and all further network plots are determined by
(rounded) with accuracy ∆ = 10 ms. Then, in order to
logarithms of the frequencies of particular transitions.
determine the phase space, a set of ordered distinct values
Study of the transitions between RR-intervals can be com-
RRMIN = RR(1) < RR(2) < ... < RR(K) = RRMAX is
pared to investigations of RR increments – the popular mea-
extracted. These K different values label different vertices in
sureofHRV.However,theadoptedschemeadditionallyserves
the network. This is depicted in Fig. 1 left where the first col-
as a classification with respect to the size of increments.
umn gives the sequence of RR intervals (already discretized),
Therefore,duetothenetworkrepresentationwelearnnotonly
the second column gives the ordered values from RRMIN
what kind of increments dominates in a signal but also when
to RRMAX, thus constituting the phase space of the signal.
these events take place.
The right panel shows the studied time series as a transition
network.Here,thelabelsofverticescorrespondtovaluesfrom
the phase space. Vertices are arranged from RRMIN(top) to III. RESULTS
RRMAX(bottom). An arrow between two vertices is plotted A. Group study: healthy versus patients after HTX
if the corresponding two RR-intervals represent a pair of the The classification of transitions scheme introduced in Sec.
consecutive values in the time series. II.B leads to clear distinction between the heart rhythm of
It appears that neighbors in time are often also neighbors healthy individuals and those of people after HTX. This is
in values what results that the transition network takes the shown in Fig. 3. For example, the transitions to the second
linearshape.Buttoimprovethevisualizationofthetransition and farther neighbors, in the case of healthy young persons,
properties we propose a ladder presentation of the network. occur with probability 0.5 (upper part of the left bar), while
Namely, vertices are placed alternatively in the left and right in case of people after HTX these events are quite rare.
columns. The majority of transitions in patients after HTX can
Moreover, to classify differences among the transitions we be described as no change events. Moreover the deceler-
PROCEEDINGSOFTHE7THESGCO2012,APRIL22-25,2012,KAZIMIERZDOLNY,POLAND 3
Fig. 3. Distributions of changes in consecutive RR-intervals for healthy
young people (of age: 18–26, 21 women and 14 men) and the group of
consideredpatientsafterHTX.Abbreviationsaccanddccrefertoacceleration
anddeceleration.Forotherdetails,seethemaintext.
ating or accelerating transitions occur rarely. Sequences of
monotonic increases of length 3, (i.e., sequences in which
RR < RR < RR < RR ) occurred, on average,
i i+1 i+2 i+3 Fig.4. Probabilitytofindagiventypeoftransitioninasignalfordifferent
onceinthewholesignal.Similarstatisticsholdsfordecreases. patientsafterHTX:top–nochangeortransitionstonearestneighbors; bottom
Therefore, only monotonic sequences of the length equal to –transitionstothenextneighbors.
1 (called one-step mono-transitions) or equal to 2 (two-step
mono-transitions) describe the short-time dynamics of the
heart contractions of the HTX patients. mid deceleration:
RR <RR <RR and |RR −RR |=3 or 4∆.
i i+1 i+2 i+2 i
The classification of the corresponding acceleration events
B. Transitions in individuals
goes with the changed directions of the above inequalities.
Statistics of one-step mono-transitions found for each
Probabilities of the occurrence of such two-step mono-
recording separately are presented in Fig. 4. They are com-
transitions, shown in Fig. 5, are ordered with respect to the
pared to the corresponding values calculated for young,
patient name, and restricted to recordings from patients being
healthy young persons (the first entry on horizontal axis).
lessthanabout12monthsafterthesurgery.Thisorderinghelps
The first observation from Fig. 4 top is that plotted values
to track alternations in the cardiac rhythm in the particular
seemtobeindependentofthetimeelapsedaftertheHTX.As
patient. The entry corresponding to healthy young people is
already observed, the no-change or transitions to the nearest
added for comparison. Note that the plots are in log-scale.
neighbor dominate. It means that almost all increments are
The data presented in Figs 4 and 5 give a total picture of
less then 10 ms. The transitions to the next-neighbors shown
changes in heart rhythm of a patient. Both analysis: one-step
in Fig. 4 bottom (the increments are grater than 10 ms
mono-transitionsandtwo-stepmono-transitionsmaybeuseful
but lower than 20ms) do not provide any regular picture.
inassessingtheprogressofpatient’srecovery,andpossiblyto
Moreover also differences between number of accelerations
produceanalarmingsignalthattheprogressisnotsatisfactory.
and decelerations are statistically not significant. However,
For example, Figs 4 and 5 does not provide the clear
concentrating on characteristics for each patient individually,
picture for the direction of changes of patients daw and
we get hints whether the changes are evolving towards the
boc. Therefore, via the network presentation we get the eye
healthy people characteristics or not.
catching and easily readable additional information on quality
The results obtained for the carefully selected two-step
and quantity of changes. In Figs 6, 7 we present network
mono-transitions are reported in Fig. 5. We classified the
representation for these two patients.
monotonic changes with respect to the total size of the
Thenetworksofdawpatient(Fig.6)showtherhythmafter
transition. Namely, the consecutive three RR-intervals RR ,
i 1 and 2 months after surgery. We see that networks are quite
RR and RR are quantified as:
i+1 i+2 similar, what indicates that the picture is stable. On the other
double loop: hand, the networks obtained for boc patient (Fig. 7) show
RR =RR =RR ; gradual simplification of the cardiac rhythm structure. It is
i i+1 i+2
slow deceleration: worth noting that our predictions based on the analysis of the
RR <RR <RR and |RR −RR |=2∆; constructednetworks(Figs.6and7)coincidewiththeclinical
i i+1 i+2 i+2 i
PROCEEDINGSOFTHE7THESGCO2012,APRIL22-25,2012,KAZIMIERZDOLNY,POLAND 4
Fig.7. Networksforbocpatientobtainedfromsignalsrecordedafter2and
6monthsafterHTX.
and qualification of their values. Additionally, it gives the
eye-catching picture of RR-intervals as a map from which
one can read at what RR-interval and how frequently the
particular increase occur. In this work we used this approach
Fig. 5. Log plots of the probability to observe double loop, slow (top) to observe the restitution of cardiac control in patients after
and mid (bottom ) transitions in signals of patients after HTX. To observe heart transplantation.
restitutionofcardiaccontrolinapatient,theresultsarecollectedbyapatient
name. In the case of sit patient after a month after HTX no mid transitions The arguments supporting the decision to perform HTX
occur. were different for each patient. The clinical state of every
patient was specific and, therefore, each time series should
be analyzed individually, and also the progress in the process
of the acceptance of the graft had to be evaluated for each
patientseparately.Thisevaluationwasattemptedduetoquan-
tificationandclassificationoftransitionsinthephasespaceof
his/her RR-intervals. We propose to interpret the alternations
in the number of particular type transitions, here towards
corresponding values found in the healthy people rhythms, in
theprognosisforindividualpatient.Moreover,sincesequences
of accelerations and decelerations of heart rate are considered
as a sign of autonomic control [6], then consecutive intervals
with fixed acceleration or deceleration rates give us additional
insights into the activity of the control mechanisms.
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